ECE 465 PLA Optimization Using Modified Multi-Function QM

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ECE 465 PLA Optimization Using Modified Multi-Function QM Shantanu Dutt ECE Dept. University of Illinois at Chicago Acknowledgement: Powerpoint slide & solution to magnitude comparator problem given here (next 5 slides) prepared by Sajjad Rahaman in consultation with Prof. Dutt

2-bit Magnitude Comparator EQ does not share any MT with other o/p functions. So, only NE, LT, and GT will be considered in the multiple-function QM optimizer

PI Formation Min term List 1 List 2 List 3 Flag 1 0000 αβ √ 1,3 00_1 1,3,9,11 _0_1 α PI1 2 0010 1,9 _001 PI13 2,3,6,7 0_1_ PI2 4 0100 αγ 2,3 001_ 4,6,12,14 _1_0 PI3 8 1000 2,6 0_10 PI12 8,9,12,13 1_0_ PI4 3 0011 4,6 01_0 6 0110 4,12 _100 PI11 9 1001 8,9 100_ 12 1100 8,12 1_00 PI10 7 0111 3,7 0_11 PI9 11 1011 3,11 _011 PI8 13 1101 6,7 011_ 14 1110 6,14 _110 PI7 9,11 10_1 9,13 1_01 PI6 12,13 110_ 12,14 11_0 PI5

Min-Cost Covering: PI Table Using a PI w/ fewer literals does not reduce PI cost for PLA optimization Thus each PI cost should be 1 Min-Cost Covering: PI Table fα fβ fγ cost Flag 1 2 3 4 6 7 8 9 11 12 13 14 PI1 α √ PI2 αβ PI3 PI4 αγ PI5 PI6 PI7 PI8 PI9 PI10 PI11 PI12 PI13 PI14 *1 *3 *2 *4

Min-Cost Covering: Reduced PI Table fα fβ fγ cost Flag 2 6 7 8 9 13 1 PI1 α √ PI2 αβ PI3 PI4 αγ PI6 PI7 PI9 PI10 PI12 PI13 1 C * 9 C 4 * 10 2 5 6 3 7 8

2-bit Magnitude Comparator: Final Solution Total AND gate needed for PLA = 6+4=10 compared to 12 AND gates if each o/p function is minimized individually Side Note: Since EQ = NE, no AND lines need be used in the PLA for generating the 4 MTs of EQ. NE can be complemented to generate EQ